Question

If the sum and product of the roots of the quadratic equation $a{x}^2-5x+c=0$ are both equal to $10$, then find the values of a and c.

• A. $a=\frac{1}{2},c=5$
• B. $a=\frac{1}{2},c=2$
• C. $a=\frac{1}{2},c=8$
• D. None of these

Answer 1

Answer: (A)

$a=\frac{1}{2},c=5$

$\Rightarrow$ The given quadratic equation is $a{x}^2-5x+c=0$

$\Rightarrow$ Here, $a=1,b=-5$ and $c=c$

$\Rightarrow$ Sum of the roots $=-\frac{b}{a}$

$\therefore$ $10=-\frac{(-5)}{a}$

$\therefore$ $10=\frac{5}{a}$

$\therefore$ $a=\frac{1}{2}$

$\Rightarrow$ Product of the roots $=\frac{c}{a}$

$\therefore$ $10=\frac{c}{\frac{1}{2}}$

$\therefore$ $10=2c$

$\therefore$ $c=5$